Types of Sets and Set Operations

Interactive Feed

JEE Main 2016

The Boolean Expression $(p \land \sim q) \lor q \lor (\sim p \land q)$ is equivalent to:

p \lor q

(B)

p \lor \sim q

(C)

\sim p \land q

(D)

p \land q

JEE Main 2015

LEVELJEE Main

Let A and B be two sets containing four and two elements respectively. Then the number of subsets of the set $A \times B$ , each having at least three elements is :

The negation of $\sim s \lor (\sim r \land s)$ is equivalent to :

(A)

s \lor (r \lor \sim s)

(B)

s \land r

(C)

s \land \sim r

(D)

s \land (r \land \sim s)

JEE Main 2014

LEVELJEE Main

If $X = {4^{n} - 3 n - 1 : n \in N}$ and $Y = {9 (n - 1) : n \in N}$ , where N is the set of natural numbers, then $X \cup Y$ is equal to:

The statement $\sim (p \leftrightarrow\sim q)$ is:

p \leftrightarrow q

(D)

equivalent to

\sim p \leftrightarrow q

JEE Main 2013

LEVELBoard

Consider Statement-1 : $(p \land \sim q) \land (\sim p \land q)$ is a fallacy. Statement-2 : $(p \to q) \leftrightarrow (\sim q \to\sim p)$ is a tautology.

(A)

Statement-1 is true; Statement-2 is true; Statement-2 is a correct explanation for Statement-1.

(B)

Statement-1 is true; Statement-2 is true; Statement-2 is not a correct explanation for Statement-I.

(C)

Statement-1 is true; Statement-2 is false.

(D)

Statement-1 is false; Statement-2 is true.

JEE Main 2012

LEVELBoard

The negation of the statement "If I become a teacher, then I will open a school", is :

(A)

I will become a teacher and I will not open a school.

(B)

Either I will not become a teacher or I will not open a school.

(C)

Neither I will become a teacher nor I will open a school.

(D)

I will not become a teacher or I will open a school.

JEE Main 2009

LEVELBoard

Statement-1: $\sim (p \leftrightarrow\sim q)$ is equivalent to $p \leftrightarrow q$ . Statement-2: $\sim (p \leftrightarrow\sim q)$ is a tautology

(A)

Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.

(B)

Statement-1 is true, Statement-2 is false.

(C)

Statement-1 is false, Statement-2 is true.

(D)

Statement-1 is true, Statement-2 is true, Statement-2 is a correct explanation for statement -1

JEE Main 2009

LEVELJEE Main

If A, B and C are three sets such that $A \cap B = A \cap C$ and $A \cup B = A \cup C$ , then

Let p be the statement "x is an irrational number", q be the statement "y is a transcendental number", and r be the statement "x is a rational number if y is a transcendental number". Statement-1 : r is equivalent to either q or p Statement-2 : r is equivalent to ~(p <-> q).

JEE Main 2008

LEVELBoard

The statement $p \to (q \to p)$ is equivalent to

(A)

p \to (p \to q)

(B)

p \to (p \lor q)

(C)

p \to (p \land q)

(D)

p \to (p \leftrightarrow q)

JEE Advanced 1998

LEVELBoard

In a college of 300 students every student reads 5 newspapers and every newspaper is read by 60 students. The number of newspapers is

If $X$ and $Y$ are two sets, then $X \cap (X \cup Y)^{c}$ equals.

(A)

X

(B)

Y

(C)

ϕ

Suppose $A_{1}, A_{2}, \dots, A_{30}$ are thirty sets each with five elements and $B_{1}, B_{2}, \dots, B_{n}$ are $n$ sets each with three elements. Let $⋃_{i = 1}^{30} A_{i} = ⋃_{j = 1}^{n} B_{j} = S$ . Assume that each element of $S$ belongs to exactly ten of the $A_{i}$ 's and to exactly nine of the $B_{j}$ 's. Find $n$ .

JEE Advanced 1978

LEVELBoard

An investigator interviewed 100 students to determine their preferences for the three drinks : milk ( $M$ ), coffee ( $C$ ) and tea ( $T$ ). He reported the following : 10 students had all the three drinks $M, C$ and $T$ ; 20 had $M$ and $C$ ; 30 had $C$ and $T$ ; 25 had $M$ and $T$ ; 12 had $M$ only; 5 had $C$ only; and 8 had $T$ only. Using a Venn diagram find how many did not take any of the three drinks.

JEE Advanced 1980

LEVELJEE Main

(i) Set $A$ has 3 elements, and set $B$ has 6 elements. What can be the minimum number of elements in the set $A \cup B$ ? (ii) $P, Q, R$ are subsets of a set $A$ . Is the following equality true? $R \times (P^{c} \cup Q^{c})^{c} = (R \times P) \cap (R \times Q)$ ?

JEE Main 2017

LEVELBoard

The following statement $(p \to q) \to [(\sim p \to q) \to q]$ is:

\sim p \to q

(C)

equivalent to

p \to\sim q

(D)

a fallacy

JEE Main 2018 (Paper 1)

LEVELBoard

The Boolean expression $\sim (p \lor q) \lor (\sim p \land q)$ is equivalent to :

(A)

\sim q

(B)

\sim p

(C)

(D)

JEE Main 2018 (15 April Shift 1)

LEVELBoard

If $(P \land \sim q) \land (p \land r) \to\sim p \lor q$ is false, then the truth values of $p, q$ and $r$ are respectively

JEE Main 2019 (9 January)

LEVELJEE Main

If the Boolean expression $(p \oplus q) \land (\sim p ⊙ q)$ is equivalent to $p \land q$ , where $\oplus, ⊙ \in {\land, \lor}$ , then the ordered pair $(\oplus, ⊙)$ is:

(A)

(\land, \lor)

(B)

(\lor, \lor)

(C)

(\land, \land)

(D)

(\lor, \land)

JEE Main 2019 (10 January Shift 1)

LEVELJEE Main

In a class of 140 students numbered 1 to 140, all even numbered students opted mathematics course, those whose number is divisible by 3 opted Physics course and those whose number is divisible by 5 opted Chemistry course. Then the number of students who did not opt for any of the three courses is :

JEE Main 2019 (9 January)

LEVELBoard

The logical statement $[\sim (\sim p \lor q) \lor (p \land r)] \land (\sim q \land r)$ is equivalent to:

(A)

(p \land r) \land \sim q

(B)

(\sim p \land \sim q) \land r

(C)

\sim p \lor r

(D)

(p \land \sim q) \lor r

JEE Main 2019 (12 January)

LEVELBoard

The expression $\sim (p \to q)$ is logically equivalent to :

(A)

\sim p \land \sim q

(B)

p \land q

(C)

\sim p \land q

(D)

p \land \sim q

JEE Main 2019 (12 January Shift 1)

LEVELJEE Main

The Boolean expression $((p \land q) \lor (p \land \sim q)) \lor (\sim p \land \sim q)$ is equivalent to:

(A)

p \land (\sim q)

(B)

p \lor (\sim q)

(C)

(\sim p) \lor (\sim q)

(D)

p \land q

JEE Main 2019 (11 January)

LEVELBoard

If $q$ is false and $p \land q \leftrightarrow r$ is true, then which one of the following statements is a tautology?

(A)

(p \lor r) \to (p \land r)

(B)

p \lor r

(C)

p \land r

(D)

(p \land r) \to (p \lor r)

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The Boolean Expression (p∧∼q)∨q∨(∼p∧q) is equivalent to:

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Let A and B be two sets containing four and two elements respectively. Then the number of subsets of the set A×B, each having at least three elements is :

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The negation of ∼s∨(∼r∧s) is equivalent to :

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } If X={4n−3n−1:n∈N} and Y={9(n−1):n∈N}, where N is the set of natural numbers, then X∪Y is equal to:

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The statement ∼(p↔∼q) is:

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Consider Statement-1 : (p∧∼q)∧(∼p∧q) is a fallacy. Statement-2 : (p→q)↔(∼q→∼p) is a tautology.

The negation of the statement "If I become a teacher, then I will open a school", is :

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Statement-1: ∼(p↔∼q) is equivalent to p↔q. Statement-2: ∼(p↔∼q) is a tautology

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } If A, B and C are three sets such that A∩B=A∩C and A∪B=A∪C, then

Let p be the statement "x is an irrational number", q be the statement "y is a transcendental number", and r be the statement "x is a rational number if y is a transcendental number". Statement-1 : r is equivalent to either q or p Statement-2 : r is equivalent to ~(p <-> q).

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The statement p→(q→p) is equivalent to

In a college of 300 students every student reads 5 newspapers and every newspaper is read by 60 students. The number of newspapers is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } If X and Y are two sets, then X∩(X∪Y)c equals.

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The following statement (p→q)→[(∼p→q)→q] is:

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The Boolean expression ∼(p∨q)∨(∼p∧q) is equivalent to :

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } If (P∧∼q)∧(p∧r)→∼p∨q is false, then the truth values of p,q and r are respectively

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } If the Boolean expression (p⊕q)∧(∼p⊙q) is equivalent to p∧q, where ⊕,⊙∈{∧,∨}, then the ordered pair (⊕,⊙) is:

In a class of 140 students numbered 1 to 140, all even numbered students opted mathematics course, those whose number is divisible by 3 opted Physics course and those whose number is divisible by 5 opted Chemistry course. Then the number of students who did not opt for any of the three courses is :

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The logical statement [∼(∼p∨q)∨(p∧r)]∧(∼q∧r) is equivalent to:

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The expression ∼(p→q) is logically equivalent to :

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The Boolean expression ((p∧q)∨(p∧∼q))∨(∼p∧∼q) is equivalent to:

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } If q is false and p∧q↔r is true, then which one of the following statements is a tautology?

The Boolean Expression $(p \land \sim q) \lor q \lor (\sim p \land q)$ is equivalent to:

Let A and B be two sets containing four and two elements respectively. Then the number of subsets of the set $A \times B$ , each having at least three elements is :

The negation of $\sim s \lor (\sim r \land s)$ is equivalent to :

If $X = {4^{n} - 3 n - 1 : n \in N}$ and $Y = {9 (n - 1) : n \in N}$ , where N is the set of natural numbers, then $X \cup Y$ is equal to:

The statement $\sim (p \leftrightarrow\sim q)$ is:

Consider Statement-1 : $(p \land \sim q) \land (\sim p \land q)$ is a fallacy. Statement-2 : $(p \to q) \leftrightarrow (\sim q \to\sim p)$ is a tautology.

Statement-1: $\sim (p \leftrightarrow\sim q)$ is equivalent to $p \leftrightarrow q$ . Statement-2: $\sim (p \leftrightarrow\sim q)$ is a tautology

If A, B and C are three sets such that $A \cap B = A \cap C$ and $A \cup B = A \cup C$ , then

The statement $p \to (q \to p)$ is equivalent to

If $X$ and $Y$ are two sets, then $X \cap (X \cup Y)^{c}$ equals.

The following statement $(p \to q) \to [(\sim p \to q) \to q]$ is:

The Boolean expression $\sim (p \lor q) \lor (\sim p \land q)$ is equivalent to :

If $(P \land \sim q) \land (p \land r) \to\sim p \lor q$ is false, then the truth values of $p, q$ and $r$ are respectively

If the Boolean expression $(p \oplus q) \land (\sim p ⊙ q)$ is equivalent to $p \land q$ , where $\oplus, ⊙ \in {\land, \lor}$ , then the ordered pair $(\oplus, ⊙)$ is:

The logical statement $[\sim (\sim p \lor q) \lor (p \land r)] \land (\sim q \land r)$ is equivalent to:

The expression $\sim (p \to q)$ is logically equivalent to :

The Boolean expression $((p \land q) \lor (p \land \sim q)) \lor (\sim p \land \sim q)$ is equivalent to:

If $q$ is false and $p \land q \leftrightarrow r$ is true, then which one of the following statements is a tautology?